\documentclass{standalone}

\usepackage{newtxtext,newtxmath}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing, angles, quotes, shapes, patterns, arrows.meta, bending, positioning}

\begin{document}
        \begin{tikzpicture}[scale = 0.8]
            \fill[gray!20] (3.75,0) -- (3.75,10.025) -- (250/35,10.025) -- (250/35,0) -- cycle;
            \draw[thick] (0,10) node[left]{1}  -- (0,0) node[midway, left=25pt, rotate=90, anchor=center]{Low-Ability Incumbents' Policy Decision $\sigma$} node[anchor=north east]{0} -- (10,0) node[midway,below=20pt]{Incumbent's Prior Expected Ability $\kappa$} node[right]{1};
            \draw[smooth, variable = \x, thick, dashed, domain = 0:3, red] plot({\x}, {10 - (28/3) * ( (\x) / (10 - \x))+0.05});
            \draw[smooth, variable = \x, thick, dashed, domain = 3:50/12, red] plot({\x}, {(14) * ( (\x) / (10 - \x))+0.1});
            \draw[thick, dotted] (250/35,10) -- (250/35, 0) node[below=2.5pt, anchor=north, scale=0.75]{$\frac{\underline{\kappa}}{\underline{\kappa} + \left(1 - \underline{\kappa}\right) \pi}$};
            \draw[red, dashed, thick] (50/12,10.03) -- (10,10.03);
            \draw[smooth, variable = \x, thick, domain = 0:3] plot({\x}, {10 - (28/3) * ( (\x) / (10 - \x))});
            \draw[smooth, variable = \x, thick, domain = 3:3.75] plot({\x}, {(14) * ( (\x) / (10 - \x))});
            \draw[smooth, variable = \x, thick, domain = 3.75:6] plot({\x}, {10 - (16/6) * ( (\x) / (10 - \x))});
            \draw[smooth, variable = \x, thick, domain = 6:250/35] plot({\x}, {(4) * ( (\x) / (10 - \x))});
            \draw[thick] (250/35,10) -- (10,10);
            \draw[thick,dotted] (3.75,0) node[below=2.5pt, anchor=north, scale=0.75]{$\frac{\underline{\kappa} \gamma}{\pi \underline{\kappa} + \left(1 - \pi\right) \gamma}$} -- (3.75,8.4);
            \draw[thick,-{Stealth}] (10.5,8) -- (10.5,2) node[midway, rotate=90, anchor=north, align=center,  yshift=-5pt]{More Policy Distortions};
        \end{tikzpicture}
\end{document}